A common approach to the measurement of mass flow rate of solid particles in a pneumatic conveying system has been to measure the volumetric flow rate (Q) or the bulk velocity (V) of the mixture, measure the bulk density (.rho.) of the mixture, and then combine the two measurements in order to determine the mass flow rate (m) of the mixture: EQU m=.rho.Q=.rho.VA
where A is equal to the cross-sectional area of the pipe.
Direct measurement of the volumetric flow rate is complicated by the velocity of the particles being different from that of the air, which is known as "slip velocity". The slip velocity of an entrained solid particle depends mainly on the size and shape of the particles within the same transport system. It is extremely difficult, however, to measure with reasonable accuracy the slip velocities of all the individual particles in any flow system. Attempts have been made to estimate the "average" slip velocity of the particles, however, this approach requires knowledge of the particle size distribution, which is not readily done in-situ. Moreover, determination of the bulk density of the mixture is not a straightforward operation because of the spatial and temporal mal-distribution of the particles. Accordingly, the synthesizing approach has not been successful.
In an earlier known form of a reaction mass flowmeter the reaction force generated by the flow momentum is measurable by one or more strain gauges attached to the flexure point of a 90 degree elbow concentrically placed inside another elbow. The reacting inside elbow is fixed at the upstream end, and the downstream end is unsupported so that it can translate in response to the flow momentum and vibrate freely at its natural frequency. The steady output of the strain gauge is a measure of the flow momentum, while the fluctuating component can be analyzed for its natural frequency, which is a function of the density of the mixture passing through the elbow section. While such an arrangement can be expected to work well with relatively dense mixtures, such as coal slurries of water or oil, it is not considered to be practical for lightly loaded pneumatic systems such as pulverized coal transport lines, at least partially due to the fact that the large mass of the elbow compared to the relatively small changes in the density makes such a system too insensitive to be useful.